Question

triangle abc is created by dilating triangle a. what is the length of ab?

Explanation:

1. First, assume the coordinates of points \(A\) and \(B\) from the graph:

• Let's assume \(A=(4,2)\) and \(B=(8,4)\).
• The distance - formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).

1. Then, identify the values of \(x_1,y_1,x_2,y_2\):

• Here, \(x_1 = 4,y_1 = 2,x_2 = 8,y_2 = 4\).
• Substitute these values into the distance - formula:
• \(d=\sqrt{(8 - 4)^2+(4 - 2)^2}\).
• First, calculate the values inside the square - root: \((8 - 4)^2=4^2 = 16\) and \((4 - 2)^2=2^2 = 4\).
• Then, \(d=\sqrt{16 + 4}=\sqrt{20}\).
• Simplify \(\sqrt{20}=\sqrt{4\times5}=2\sqrt{5}\).

Step1: Identify coordinates

Let \(A=(4,2)\), \(B=(8,4)\)

Step2: Apply distance formula

\(d=\sqrt{(8 - 4)^2+(4 - 2)^2}\)

Step3: Calculate squares

\(d=\sqrt{16 + 4}\)

Step4: Simplify square - root

\(d = 2\sqrt{5}\)

Answer:

\(2\sqrt{5}\)